Finite Group Databasebeta

← D11×#2483 #14922693

Subgroups — D11×#2483 #14922693

Order 2816.

4382 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C4×D11C212yesmaximal
2#13072897C211yesmaximal, characteristic, complemented
3#13072896C214yesmaximal, complemented
4#13072895C214yesmaximal, complemented
5#13072894C212yesmaximal, complemented
6#13072893C214yesmaximal, complemented
7D11×#397C214yesmaximal, complemented
8D11×#385C214yesmaximal, complemented
9D11×#381C214yesmaximal, complemented
10D11×#379C211yesmaximal, characteristic
11C11×#2483C211yesmaximal, characteristic, complemented
12C25×D11C2211yescharacteristic
13C23×C4×D11C2212yes—
14C23×C4×D11C2212yes—
15C22×C11×C22⋊C4C2212yes—
16C22×C22⋊Dic11C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C2×C4⋊C4×D11C2214yescomplemented
20C2×C22⋊C4×D11—216no—
21C2×C22⋊C4×D11C2214yes—
22C2×C22⋊C4×D11C2214yes—
23C2×C22⋊C4×D11C2214yes—
24C2×C22⋊C4×D11C2214yes—
25C2×C22⋊C4×D11C2214yes—
26C2×C22⋊C4×D11C2212yes—
27C11×#397C2214yescomplemented
28C11×#385C2214yescomplemented
29C11×#381C2214yescomplemented
30C11×#379C2211yescharacteristic
31#10622860C2211yescharacteristic
32#10622824C2214yescomplemented
33#10622823C2214yescomplemented
34#10622606C2214yescomplemented
35#10622602C2218yescomplemented
36#10622568C2214yes—
37#10622568C2212yes—
38#10622566C2214yescomplemented
39#10622565C2218yescomplemented
40#10622563C2214yescomplemented
41#10622559C2214yescomplemented
42#10622556C2214yescomplemented
43#10622556C2214yescomplemented
44#10622288C2218yescomplemented
45#10622287C2214yescomplemented
46#10622281C2218yescomplemented
47#10622277C2218yescomplemented
48#10622277C2218yescomplemented
49D11×#95C2214yescomplemented
50D11×#95C2218yescomplemented
51C25×C11C2311yescharacteristic
52C24×D11—216no—
53C24×D11—44no—
54C24×D11D418yes—
55C24×D11C2311yescharacteristic
56C24×D11C2311yescharacteristic
57C24×D11C2312yes—
58C24×D11C2312yes—
59C23×C4×C11C2312yes—
60C23×C4×C11C2312yes—
61C23×Dic11C2312yes—
62C23×Dic11C2312yes—
63C22×C4×D11—28no—
64C22×C4×D11—28no—
65C22×C4×D11—216no—
66C22×C4×D11—48no—
67C22×C4×D11C2314yes—
68C22×C4×D11C2314yes—
69C22×C4×D11C2314yes—
70C22×C4×D11C2314yes—
71C22×C4×D11C2314yes—
72C2×C11×C4⋊C4C2314yescomplemented
73C2×C11×C22⋊C4—28no—
74C2×C11×C22⋊C4C2314yes—
75C2×C11×C22⋊C4C2314yes—
76C2×C11×C22⋊C4C2314yes—
77C2×C11×C22⋊C4C2312yes—
78C2×C22⋊Dic11—28no—
79C2×C22⋊Dic11C2314yes—
80C2×C22⋊Dic11C2314yes—
81C2×C22⋊Dic11C2314yes—
82C2×C22⋊Dic11C2312yes—
83C2×(C2×D11)⋊C4—28no—
84C2×(C2×D11)⋊C4—28no—
85C2×(C2×D11)⋊C4C2314yes—
86C2×(C2×D11)⋊C4C2314yes—
87C2×(C2×D11)⋊C4C2314yes—
88C2×(C2×D11)⋊C4C2314yes—
89C2×(C2×D11)⋊C4C2318yes—
90C2×(C2×D11)⋊C4C2314yes—
91C2×C4⋊Dic11C2314yescomplemented
92C2×Dic11⋊C4C2318yescomplemented
93C4⋊C4×D11—48no—
94C22⋊C4×D11—216no—
95C22⋊C4×D11—216no—
96C22⋊C4×D11—216no—
97C22⋊C4×D11—216no—
98C22⋊C4×D11—216no—
99C22⋊C4×D11—44no—
100C11×#95C2314yescomplemented
101C11×#95C2318yescomplemented
102C11⋊#95C2318yescomplemented
103C11⋊#95C2314yescomplemented
104C11⋊#95C2318yescomplemented
105C11⋊#95C2318yescomplemented
106C11⋊#95C2318yescomplemented
107C2×#2483—111nomaximal, Sylow
108C24×C11—28no—
109C24×C11—42no—
110C24×C11C2×D414yes—
111C24×C11C2411yescharacteristic
112C24×C11C2412yes—
113C23×D11—28no—
114C23×D11—28no—
115C23×D11—28no—
116C23×D11—264no—
117C23×D11—28no—
118C23×D11—28no—
119C23×D11—28no—
120C23×D11—24no—
121C23×D11—416no—
122C23×D11—42no—
123C23×D11—44no—
124C23×D11—464no—
125C23×D11C2×D414yes—
126C23×D11C2×D414yes—
127C23×D11C2×D418yes—
128C23×D11C2×D418yes—
129C23×D11#41116yes—
130C23×D11C2411yescharacteristic
131C23×D11C2412yes—
132C23×D11C2411yescharacteristic
133C22×C4×C11—24no—
134C22×C4×C11—24no—
135C22×C4×C11—28no—
136C22×C4×C11—44no—
137C22×C4×C11C2414yes—
138C22×C4×C11C2414yes—
139C22×C4×C11C2414yes—
140C22×Dic11—24no—
141C22×Dic11—24no—
142C22×Dic11—28no—
143C22×Dic11—44no—
144C22×Dic11C2414yes—
145C22×Dic11C2414yes—
146C22×Dic11C2414yes—
147C2×C4×D11—28no—
148C2×C4×D11—28no—
149C2×C4×D11—28no—
150C2×C4×D11—28no—
151C2×C4×D11—216no—
152C2×C4×D11—216no—
153C2×C4×D11—216no—
154C2×C4×D11—28no—
155C2×C4×D11—216no—
156C2×C4×D11—48no—
157C2×C4×D11—432no—
158C2×C4×D11—432no—
159C11×C4⋊C4—44no—
160C11×C22⋊C4—28no—
161C11×C22⋊C4—28no—
162C11×C22⋊C4—28no—
163C11×C22⋊C4—42no—
164C22⋊Dic11—28no—
165C22⋊Dic11—28no—
166C22⋊Dic11—28no—
167C22⋊Dic11—42no—
168(C2×D11)⋊C4—28no—
169(C2×D11)⋊C4—28no—
170(C2×D11)⋊C4—28no—
171(C2×D11)⋊C4—28no—
172(C2×D11)⋊C4—216no—
173(C2×D11)⋊C4—44no—
174C4⋊Dic11—44no—
175Dic11⋊C4—48no—
176C23×C22⋊C4—112no—
177#2483—114no—
178#2483—114no—
179#2483—114no—
180#2483—111no—
181#2483—112no—
182#2483D1111yescharacteristic, direct product factor
183C2×#397—114no—
184C2×#385—114no—
185C2×#381—114no—
186C2×#379—111no—
187C23×C11—24no—
188C23×C11—24no—
189C23×C11—216no—
190C23×C11—24no—
191C23×C11—22no—
192C23×C11—44no—
193C23×C11—416no—
194C23×C11C22×D412yes—
195C23×C11C22×D414yes—
196C23×C11C2×#4118yes—
197C23×C11C2511yescharacteristic
198C22×D11—24no—
199C22×D11—24no—
200C22×D11—216no—
201C22×D11—216no—
202C22×D11—264no—
203C22×D11—216no—
204C22×D11—24no—
205C22×D11—22no—
206C22×D11—216no—
207C22×D11—216no—
208C22×D11—216no—
209C22×D11—28no—
210C22×D11—44no—
211C22×D11—48no—
212C22×D11—416no—
213C22×D11—4128no—
214C22×D11—432no—
215C22×D11—416no—
216C22×D11#123132yes—
217C22×D11C22×D412yes—
218C22×D11C22×D414yes—
219C22×D11C22×D412yes—
220C22×D11C2×#4118yes—
221C22×D11C2×#4118yes—
222C22×D11H(5,𝔽2)14yes—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—28no—
226C2×C4×C11—28no—
227C2×C4×C11—28no—
228C2×C4×C11—24no—
229C2×C4×C11—48no—
230C2×C4×C11—48no—
231C2×Dic11—24no—
232C2×Dic11—24no—
233C2×Dic11—28no—
234C2×Dic11—28no—
235C2×Dic11—24no—
236C2×Dic11—28no—
237C2×Dic11—48no—
238C2×Dic11—48no—
239C4×D11—416no—
240C4×D11—416no—
241C4×D11—416no—
242C4×D11—416no—
243C4×D11—416no—
244C26—111no—
245C24×C4—112no—
246C24×C4—112no—
247C22×C4⋊C4—114no—
248C22×C22⋊C4—112no—
249C22×C22⋊C4—112no—
250C22×C22⋊C4—112no—
251C22×C22⋊C4—114no—
252C22×C22⋊C4—114no—
253C22×C22⋊C4—114no—
254C22×C22⋊C4—114no—
255C22×C22⋊C4—114no—
256C22×C22⋊C4—112no—
257C22×C22⋊C4—2216no—
258C22×C22⋊C4C2×D1112yes—
259#397—114no—
260#397—118no—
261#397—114no—
262#397—114no—
263#397—118no—
264#397C2×D1114yescomplemented
265#385—114no—
266#385—118no—
267#385—114no—
268#385—114no—
269#385—118no—
270#385C2×D1114yescomplemented
271#381—114no—
272#381—114no—
273#381—114no—
274#381—118no—
275#381—118no—
276#381C2×D1114yescomplemented
277#379—111no—
278#379—114no—
279#379—112no—
280#379C2×D1111yescharacteristic
281C2×#95—114no—
282C2×#95—118no—
283C22×C11—24no—
284C22×C11—24no—
285C22×C11—216no—
286C22×C11—24no—
287C22×C11—22no—
288C22×C11—416no—
289C22×C11—44no—
290C22×C11C2×#12318yes—
291C22×C11C23×D411yescharacteristic
292C22×C11C22×#4114yes—
293C22×C11C2×H(5,𝔽2)12yes—
294C2×D11—24no—
295C2×D11—24no—
296C2×D11—216no—
297C2×D11—264no—
298C2×D11—24no—
299C2×D11—22no—
300C2×D11—416no—
301C2×D11—432no—
302C2×D11—44no—
303C2×D11—416no—
304C2×D11C2×#12318yes—
305C2×D11C2×#12318yes—
306C2×D11#53414yes—
307C2×D11#551116yes—
308C4×C11—44no—
309C4×C11—44no—
310C4×C11—44no—
311Dic11—44no—
312Dic11—44no—
313Dic11—44no—
314C25—112no—
315C25—111no—
316C25—118no—
317C25—111no—
318C25—112no—
319C25—2216no—
320C25—444no—
321C25C22×D1111yescharacteristic
322C23×C4—112no—
323C23×C4—112no—
324C23×C4—114no—
325C23×C4—114no—
326C23×C4—114no—
327C23×C4—114no—
328C23×C4—114no—
329C23×C4—228no—
330C23×C4—228no—
331C23×C4—2216no—
332C23×C4—448no—
333C23×C4C22×D1112yes—
334C23×C4C22×D1112yes—
335C2×C4⋊C4—118no—
336C2×C4⋊C4—114no—
337C2×C4⋊C4—448no—
338C2×C4⋊C4C22×D1114yescomplemented
339C2×C22⋊C4—28no—
340C2×C22⋊C4—114no—
341C2×C22⋊C4—114no—
342C2×C22⋊C4—114no—
343C2×C22⋊C4—114no—
344C2×C22⋊C4—114no—
345C2×C22⋊C4—114no—
346C2×C22⋊C4—114no—
347C2×C22⋊C4—118no—
348C2×C22⋊C4—112no—
349C2×C22⋊C4—114no—
350C2×C22⋊C4—2216no—
351C2×C22⋊C4—2216no—
352C2×C22⋊C4—2216no—
353C2×C22⋊C4—2216no—
354C2×C22⋊C4—2216no—
355C2×C22⋊C4—228no—
356C2×C22⋊C4—228no—
357C2×C22⋊C4—228no—
358C2×C22⋊C4—444no—
359C2×C22⋊C4C22×D1114yes—
360C2×C22⋊C4C22×D1114yes—
361C2×C22⋊C4C22×D1114yes—
362C2×C22⋊C4C22×D1112yes—
363#95—114no—
364#95—118no—
365#95—118no—
366#95—118no—
367#95—118no—
368#95C22×D1114yescomplemented
369#95C22×D1118yescomplemented
370C2×C11—28no—
371C2×C11—42no—
372C2×C11C22×#12312yes—
373C2×C11C2×#53411yescharacteristic
374C2×C11C2×#55114yes—
375D11—28no—
376D11—42no—
377D11#248318yesdirect product factor
378C24—28no—
379C24—42no—
380C24—111no—
381C24—118no—
382C24—1116no—
383C24—112no—
384C24—114no—
385C24—111no—
386C24—114no—
387C24—118no—
388C24—228no—
389C24—228no—
390C24—224no—
391C24—228no—
392C24—2264no—
393C24—228no—
394C24—228no—
395C24—228no—
396C24—444no—
397C24—442no—
398C24—4416no—
399C24—4464no—
400C24D4×D1114yes—
401C24C23×D1111yescharacteristic
402C24C23×D1112yes—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—28no—
406C22×C4—44no—
407C22×C4—114no—
408C22×C4—114no—
409C22×C4—114no—
410C22×C4—228no—
411C22×C4—228no—
412C22×C4—228no—
413C22×C4—228no—
414C22×C4—2216no—
415C22×C4—228no—
416C22×C4—2216no—
417C22×C4—2216no—
418C22×C4—2216no—
419C22×C4—224no—
420C22×C4—224no—
421C22×C4—228no—
422C22×C4—448no—
423C22×C4—4432no—
424C22×C4—4432no—
425C22×C4—444no—
426C22×C4C23×D1114yes—
427C22×C4C23×D1114yes—
428C22×C4C23×D1114yes—
429C4⋊C4—44no—
430C4⋊C4—448no—
431C4⋊C4—444no—
432C22⋊C4—28no—
433C22⋊C4—28no—
434C22⋊C4—28no—
435C22⋊C4—42no—
436C22⋊C4—228no—
437C22⋊C4—228no—
438C22⋊C4—228no—
439C22⋊C4—228no—
440C22⋊C4—2216no—
441C22⋊C4—228no—
442C22⋊C4—228no—
443C22⋊C4—228no—
444C22⋊C4—444no—
445C22⋊C4—442no—
446C11C2×#248311yescharacteristic, complemented, Sylow
447C23—24no—
448C23—24no—
449C23—216no—
450C23—24no—
451C23—22no—
452C23—44no—
453C23—416no—
454C23—112no—
455C23—118no—
456C23—114no—
457C23—1132no—
458C23—114no—
459C23—118no—
460C23—112no—
461C23—2216no—
462C23—2216no—
463C23—2264no—
464C23—2216no—
465C23—2216no—
466C23—2216no—
467C23—228no—
468C23—224no—
469C23—224no—
470C23—2216no—
471C23—224no—
472C23—222no—
473C23—448no—
474C23—444no—
475C23—4432no—
476C23—4416no—
477C23—44128no—
478C23—4416no—
479C23C2×D4×D1112yes—
480C23C2×D4×D1114yes—
481C23#41×D1118yes—
482C23C24×D1111yescharacteristic
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—28no—
486C2×C4—28no—
487C2×C4—24no—
488C2×C4—28no—
489C2×C4—48no—
490C2×C4—48no—
491C2×C4—224no—
492C2×C4—224no—
493C2×C4—228no—
494C2×C4—228no—
495C2×C4—224no—
496C2×C4—228no—
497C2×C4—4416no—
498C2×C4—4416no—
499C2×C4—4416no—
500C2×C4—4416no—
501C2×C4—4416no—
502C2×C4—448no—
503C2×C4—448no—
504C22—24no—
505C22—24no—
506C22—216no—
507C22—22no—
508C22—24no—
509C22—416no—
510C22—44no—
511C22—114no—
512C22—118no—
513C22—1116no—
514C22—118no—
515C22—2264no—
516C22—224no—
517C22—224no—
518C22—2216no—
519C22—222no—
520C22—224no—
521C22—4432no—
522C22—4416no—
523C22—4416no—
524C22—444no—
525C22D11×#12318yes—
526C22C22×D4×D1111yescharacteristic
527C22C2×#41×D1114yes—
528C22D11×H(5,𝔽2)12yes—
529C4—44no—
530C4—44no—
531C4—44no—
532C4—444no—
533C4—444no—
534C4—444no—
535C2—28no—
536C2—42no—
537C2—118no—
538C2—228no—
539C2—442no—
540C2C2×D11×#12312yes—
541C2D11×#53411yescharacteristic
542C2D11×#55114yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2483C2
prime radicalC25×D11C22
hypercenter#2483D11
hypocenterC11C2×#2483
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2483

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #13072897C2semidirect
3. #13072896C2semidirect
4. #13072895C2semidirect
5. #13072894C2semidirect
6. #13072893C2semidirect
7. D11×#397C2semidirect
8. D11×#385C2semidirect
9. D11×#381C2semidirect
11. C11×#2483C2semidirect
19. C2×C4⋊C4×D11C22semidirect
27. C11×#397C22semidirect
28. C11×#385C22semidirect
29. C11×#381C22semidirect
32. #10622824C22semidirect
33. #10622823C22semidirect
34. #10622606C22semidirect
35. #10622602C22semidirect
38. #10622566C22semidirect
39. #10622565C22semidirect
40. #10622563C22semidirect
41. #10622559C22semidirect
42. #10622556C22semidirect
43. #10622556C22semidirect
44. #10622288C22semidirect
45. #10622287C22semidirect
46. #10622281C22semidirect
47. #10622277C22semidirect
48. #10622277C22semidirect
49. D11×#95C22semidirect
50. D11×#95C22semidirect
72. C2×C11×C4⋊C4C23semidirect
91. C2×C4⋊Dic11C23semidirect
92. C2×Dic11⋊C4C23semidirect
100. C11×#95C23semidirect
101. C11×#95C23semidirect
102. C11⋊#95C23semidirect
103. C11⋊#95C23semidirect
104. C11⋊#95C23semidirect
105. C11⋊#95C23semidirect
106. C11⋊#95C23semidirect
182. #2483D11direct (N × H)
264. #397C2×D11semidirect
270. #385C2×D11semidirect
276. #381C2×D11semidirect
338. C2×C4⋊C4C22×D11semidirect
368. #95C22×D11semidirect
369. #95C22×D11semidirect
377. D11#2483direct (N × H)
446. C11C2×#2483semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C22⋊C4×D112
#130728972
#130728962
#130728952
#130728942
#130728932
D11×#3972
D11×#3852
D11×#3812
D11×#3792
C11×#24832
C2×#248311